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Problem on the Mathematical Plaque at Gokonomiya Shrine (Fushimi, Kyoto)

Author: tonagaiExecutions: 763
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This is a problem from a mathematical plaque at Gokō-gū Shrine in Fushimi, Kyoto. There are three squares labeled A, B, andC, and the sum of their areas equals a certain value;
the cube of the side length of A, the fifth power of the side length of B, and the seventh power of the side length of C also equal a certain value; furthermore, the difference between the side length of A and the side length of B is equal to
the difference between the side length of B and the side length of C.What are the lengths of the sides of squares A, B, and C? Note that A > B > C.
Sum of Areas
(One side of A)^3 + (one side of B)^5 + (one side of C)^7
One side of Figure A 
One side of side B 
One side of Group C 

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Problem on the Mathematical Plaque at Gokonomiya Shrine (Fushimi, Kyoto) | Keisan